For any three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ show that $\overrightarrow{a}\times(\overrightarrow{b}+\overrightarrow{c})+\overrightarrow{b}\times(\overrightarrow{c}+\overrightarrow{a})+\overrightarrow{c}\times(\overrightarrow{a}+\overrightarrow{b})=\overrightarrow{0}$